Linear transformation conditions?

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1. $L(u+v) = L(u) + L(v)$ for every $u$ and $v$
2. $L(cu) = cL(u)$ for any $u\in V$, and $ c$ any real number

Do both conditions have to meet or can we say a vector is a linear transformation of the other if just one of these conditions meet? Or is it that if one meets, the other also will (which is not likely)

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1 Answer

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It must meet both conditions for a transformation to be called linear. Meeting one of these conditions doesn't necessarily imply that the other condition will hold.

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